Mason Adams
Geometry teacher | Tutor for 5 years
With a major in Geometry from Hamilton College, my passion lies in unraveling the intricacies of shapes and spaces. I thrive on guiding students through the maze of geometric concepts, making the abstract tangible and the complex clear. My approach fosters not just understanding, but also a deep appreciation for the elegance of geometry. Let's embark on a journey where angles, lines, and figures come to life, paving the way for newfound confidence and mastery in mathematics.
Questions
A triangle has two corners of angles #pi /8# and #(2pi)/3 #. What are the complement and supplement of the third corner?
(a) Can Kayla conclude that and are similar? Why or why not? (b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain.
What is the equation of the circle with a center at #(2 ,6 )# and a radius of #3 #?
A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #9 #, #4 #, and #5 #, respectively. What is the rectangle's area?
Triangle A has an area of #5 # and two sides of lengths #6 # and #7 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?
A line segment has endpoints at #(1 ,5 )# and #(0 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
Cups A and B are cone shaped and have heights of #12 cm# and #15 cm# and openings with radii of #6 cm# and #4 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #(5pi)/12 #, and the triangle's area is #28 #. What is the area of the triangle's incircle?
A cone has a height of #14 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #5 cm# from the base, what would the surface area of the bottom segment be?
When are similar figures congruent?
A triangle has corners at #(6 , 3 )#, #(3 ,5 )#, and #(2 ,9 )#. What is the radius of the triangle's inscribed circle?
A triangle has corners at #(2 , 1 )#, #(3 ,4 )#, and #(1 ,2 )#. What is the radius of the triangle's inscribed circle?
Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(7 ,2 )# and an area of #64 pi#. Do the circles overlap?
Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?
How do you find the interior angle of a polygon?
A circle has a chord that goes from #( pi)/3 # to #(2 pi) / 3 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?
A clock tower has a circular clock face with an area of #144pi# square feet. What is the diameter of the clock face?
How do you write an equation of a circle with center at (0,0), d=12?
How are isosceles and equilateral triangles the same?